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    Dzyaloshinskii-Moriya–driven instabilities in square-kagome quantum antiferromagnets

    Leonid S. Taran1,*, Arnaud Ralko2,3,*, Fedor V. Temnikov1,*, Vladimir V. Mazurenko4, Sergey V. Streltsov1,3,4, and Yasir Iqbal3,†

    • *These authors contributed equally to this work.
    • †Contact author: yiqbal@physics.iitm.ac.in

    Phys. Rev. B 114, 074414 – Published 10 August, 2026

    DOI: https://doi.org/10.1103/9p42-vt6m

    Abstract

    Decorated square-kagome quantum antiferromagnets provide a natural setting in which strong frustration, lattice decoration, and spin-orbit-induced anisotropy compete on comparable energy scales. Here we show, within a Schwinger-boson mean-field treatment of the realistic Hamiltonian, that the coupling J10 linking the decorating Cu(3) sites to the square-kagome backbone stabilizes the gapped saddle point, while symmetry-allowed Dzyaloshinskii-Moriya (DM) interactions systematically suppress the minimum spinon gap Δspinon and enhance the tendency toward boson softening. To establish this, we combine ab initio calculation of the DM vectors with a Schwinger-boson self-consistent mean-field treatment (SBMFT) extended to include the triplet hopping and pairing channels required by explicit spin-rotation-symmetry breaking. As a benchmark, the isotropic square-kagome Heisenberg model exhibits four competing low-energy saddle points distinguished by their Wilson-loop fluxes and by characteristic static and dynamical structure-factor fingerprints. A minimal DM perturbation does not qualitatively reshape this competing landscape, but already enhances low-energy spectral weight in the ordered saddle points. For the realistic decorated Hamiltonian, finite-size scaling of Δspinon together with momentum-resolved structure factors identifies J10 as a control parameter for the stability of the gapped mean-field regime and shows that the full symmetry-allowed DM pattern shifts the spectrum toward lower energies. Our results indicate that, within SBMFT, Na6Cu7BiO4(PO4)4Cl3 lies close to a regime where the gapped saddle point becomes soft, and provide experimentally testable predictions for anisotropy-enhanced low-energy spectral weight in decorated square-kagome materials.

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